Problem: $h(t) = 2t+6+3(g(t))$ $g(x) = x$ $f(x) = -3x+h(x)$ $ g(f(4)) = {?} $
Explanation: First, let's solve for the value of the inner function, $f(4)$ . Then we'll know what to plug into the outer function. $f(4) = (-3)(4)+h(4)$ To solve for the value of $f$ , we need to solve for the value of $h(4)$ $h(4) = (2)(4)+6+3(g(4))$ To solve for the value of $h$ , we need to solve for the value of $g(4)$ $g(4) = 4$ $g(4) = 4$ That means $h(4) = (2)(4)+6+(3)(4)$ $h(4) = 26$ That means $f(4) = (-3)(4)+26$ $f(4) = 14$ Now we know that $f(4) = 14$ . Let's solve for $g(f(4))$ , which is $g(14)$ $g(14) = 14$